NEW YORK -- Serena Williams was penalized a game for calling the chair umpire a thief during an extended argument as the US Open women's final descended into chaos, with fans booing and play delayed before Naomi Osaka wrapped up a 6-2, 6-4 victory for her first Grand Slam title.

Whether or not you agree with what went down in the US Open women's final, one thing is for sure: It's time to change the coaching rules in tennis.

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The biggest issue for Williams on the scoreboard Saturday was that she was outplayed by a younger version of herself in Osaka, a 20-year-old who is the first player from Japan to win a major singles tennis title and idolizes the 36-year-old American.

During the trophy ceremony in Arthur Ashe Stadium, thousands of fans jeered repeatedly, and both Osaka, the champion, and Williams, the runner-up in her bid for a record-tying 24th Grand Slam trophy, cried.

Williams put an arm around Osaka's shoulder and told the crowd: "I know you guys were here rooting, and I was rooting, too, but let's make this the best moment we can. ... We're going to get through this, and let's be positive. So congratulations, Naomi. No more booing."

Added Williams, with a laugh: "I really hope to continue to go and play here again. We'll see."

A teary Osaka addressed the pro-Williams crowd, saying, "I'm sorry. I know that everyone was cheering for her, and I'm sorry that it had to end like this. I just want to say thank you for watching the match. Thank you."

She added: "It was always my dream to play Serena in the US Open finals, so I'm really glad that I was able to do that. I'm really grateful that I was able to play with you. Thank you."

Serena Williams urged the crowd to make Naomi Osaka's moment a good one for her. AP Photo/Adam Hunger

Williams was fined a total of $17,000 for the three code violations on Saturday. She was fined $4,000 for receiving coaching, $3,000 for racket abuse and $10,000 for verbal abuse.

What the 2018 final will forever be remembered for is the way Williams clashed with chair umpire Carlos Ramos, demanding an apology after he initially issued a warning in the second set's second game for a code violation for receiving coaching, which is not allowed during Grand Slam matches.

The WTA released a statement after the match, urging celebration of both players while saying, "There are matters that need to be looked into."

WTA Statement on 2018 US Open Final

Congratulations to both Naomi and Serena for reaching the final at the 50th anniversary of the US Open and to Naomi for winning her first Grand Slam title. They both played superb tennis throughout the US Open. There are matters that need to be looked into that took place during the match. For tonight, it is time to celebrate these two amazing players, both of whom have great integrity. Naomi is a deserving champion, and Serena at all times plays with class and makes us proud.

The US Open later issued a statement saying that Ramos' decision was "final and not reviewable by the Tournament Referee or the Grand Slam Supervisor who were called to the court at that time."

Williams objected right away, saying she would "rather lose" than cheat. After the match, in an interview with ESPN, Williams' coach, Patrick Mouratoglou, acknowledged that he had tried to signal Williams but said he didn't think she had seen him. He added that he thinks every player gets coaching during matches.

The US Open on the Women's Final

In its own statement, the US Open recounted the moments leading up to the warning and penalties issued to Williams and said Ramos' decision to assess a third code violation "was final and not reviewable by the Tournament Referee or the Grand Slam Supervisor who were called to the court at that time."

"Well, I mean, I'm honest, I was coaching. I mean, I don't think she looked at me, so that's why she didn't even think I was. I was like 100 percent of the coaches on 100 percent of the matches, so we have to stop this hypocrite thing," Mouratoglou said. "Sascha [Bajin, Osaka's coach,] was coaching every point, too. This chair umpire was the chair umpire of most of the finals of Rafa [Nadal], and Toni's coaching every single point, and they never gave a warning. I don't really get it. It's strange."

Mouratoglou added that he had never been called for a coaching violation: "Not once in my life, and you can check the records, you'll see."

Briefly, Williams appeared to be working her way back into the match, breaking Osaka for the only time to go up 3-1 in the second set. But Williams played a poor game right after that to get broken immediately, and she smashed her racket on the court, destroying it. That drew a second code violation, automatically costing Williams a point. When she realized that the next game had started with Osaka ahead 15-love, Williams told Ramos he should have retracted the initial warning for coaching.

She resumed arguing with Ramos later, saying, "You stole a point from me. You're a thief, too."

He responded by issuing a third code violation, which results in a lost game. That made it 5-3 for Osaka.

Ramos called both players over to explain his ruling, and Williams began laughing, saying: "Are you kidding me?" She asked to speak to tournament referee Brian Earley, who walked onto the court along with a Grand Slam supervisor. Williams told them the whole episode "is not fair" and said, "This has happened to me too many times."

"To lose a game for saying that is not fair," Williams said. "There's a lot of men out here that have said a lot of things, and because they are men, that doesn't happen."

Soon thereafter, the match was over.

WTA CEO Steve Simon on Final

In a statement released on Sunday, Simon said the "WTA believes that there should be no difference in the standards of tolerance provided to the emotions expressed by men vs. women and is committed to working with the sport to ensure that all players are treated the same. We do not believe that this was done last night."

On Sunday, WTA CEO Steve Simon issued a statement saying the WTA believed that some gender bias and sexism occurred in the game, and that "further review" of the coaching rule is needed.

USTA chairman and president Katrina Adams released a statement on the final later Saturday, congratulating Williams for her "great deal of class and sportsmanship."

"This was Naomi's moment and Serena wanted her to be able to enjoy it. That was a class move from a true champion. What Serena has accomplished this year in playing her way back on to the tour is truly amazing. She continues to inspire, because she continues to strive to be the best. She owns virtually every page of the record book, but she's never been one to rest on her laurels."

It was the second Grand Slam final defeat in a row for Williams, after Wimbledon in July, as she seeks her first major title since her return to the tour after having a baby in 2017. She missed the US Open last year because her daughter, Olympia, was born during the tournament.

This was umpire Ramos' first women's singles final at the US Open. Ramos chaired the women's singles finals at the French Open in 2005 and at Wimbledon in 2018. He has chaired seven men's singles finals across all four Grand Slams and the men's singles final at the 2012 London Olympics.

Saturday's controversy was not the first involving a chair umpire at this year's Open. Alize Cornet was cited for taking off her shirt, and the United States Tennis Association issued a statement saying the chair umpire was wrong to have cited her. Nick Kyrgios received encouragement from a chair umpire during his match, and the USTA admonished him for doing so.